We analyze the susceptibility of the Internet to random faults, malicious attacks, and mixtures of faults and analyze actual Internet data, as well as simulated data created with network models. The network models generalize previous research, and allow generation of graphs ranging from uniform to preferential, and from static to introduce new metrics for analyzing the connectivity and performance of networks which improve upon metrics used in earlier research. Previous research has shown that preferential networks like the Internet are more robust to random failures compared to uniform networks. We find that preferential networks, including the Internet, are more robust only when more than 95% of failures are random faults,.